Engaging students: Classifying polygons

In my capstone class for future secondary math teachers, I ask my students to come up with ideas for engaging their students with different topics in the secondary mathematics curriculum. In other words, the point of the assignment was not to devise a full-blown lesson plan on this topic. Instead, I asked my students to think about three different ways of getting their students interested in the topic in the first place.

I plan to share some of the best of these ideas on this blog (after asking my students’ permission, of course).

This student submission again comes from my former student Samantha Smith. Her topic, from Geometry: classifying polygons.

D. 4. What are the contributions of various cultures to this topic?

Tangrams

The tangram is a puzzle game that originated in China. It has been documented that this puzzle has been played since at least the early 1800s, and even before that. By around 1817, the tangram had gained popularity in Europe and America. Its components consist of seven pieces: one square, one parallelogram, two small isosceles triangles, one medium isosceles triangle, and two large isosceles triangles. Each piece is called a tan. The shapes can be arranged into different figures. As you can see in the picture below, these pieces can be arranged in many ways. For the classroom, the teacher can give the students tans to make their own figures, or the teacher can give them a silhouette of a figure and have the students create the tangram. This is just a fun way to have the students interact with the shapes they are learning about, and experience some world culture.

B.2. How does this topic extend what your students should have learned in previous courses?

Geo-Boards

When I took Concepts of Algebra and Geometry last semester, we had a full lesson on polygons. The professor gave us a tool called a Geo-Board to model polygons using rubber bands (as pictured below). This was a really fun and short hands-on activity to engage us in the lesson. After we made our shape with the rubber band, we would go more in depth and triangulate it to find the sum of the angles in the polygon. The Geo-Board will be exciting for high school students. The teacher can name a familiar shape that the students can model on their board. Most of the shapes they will be modeling they will have worked with in many previous math courses. Another cool thing about the Geo-Board is that the students can see there is more than one way to make a polygon, as long as they have the right number of sides. Of course there are stricter rules for squares, equilateral triangles, etc.; however, students can still model those shapes on the Geo-Board while the teacher walks around and checks their work.

C. How has this topic appeared in culture?

Traffic Signs

Every day people get into cars and drive. They are expected to follow the laws of the road. One of the first things you learn in Driver’s Ed. are the different traffic signs; their colors, their shapes and what they mean. What I notice is that traffic signs are in the shapes of polygons, and their shape is important to their meaning. A stop sign is an octagon, a yield sign is a triangle, and a pedestrian crossing sign is a pentagon. Knowing these shapes can help determine what a sign means, especially if the driver is too far away to read what it says.

This is an everyday use of classifying polygons. Students do it all the time; they just might not realize it. Engaging high school students with traffic signs could prove beneficial for them in more ways than one: not just learning about shapes, but about traffic signs they will be tested on before they get their driver’s license, which is what many students are doing in high school.